3. Let X = {X1, X2, . . . , Xn} be a random sample from the probability distributionwith probability density function:(202 /x for c > 0f (x; 0) =0.otherwise.(a) Find a sufficient statistic for 0.(b) Find the maximum likelihood estimator of 0.(c) Find a pivotal function of the maximum likelihood estimator found in (b).(d) Use the pivotal function obtained in (c) to construct a 100(1– a)% confidenceinterval for 0.

Answered: Image /qna-images/answer/93d97733-a949-4868-8b47-be13169b0112.jpg

Answered: (a) Find a sufficient statistic for 0.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a sample size n=99 is drawn from a population whose standard deaviation is 11 (a) find the margin of error for a confidence interval for u (population mean). round the answer to at least three decimal places the margin of error for a 90% confidence for u (population mean) is
Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of (i) 400 and (ii) 1600. What is the effect of the sample size? (i) Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of 400. 9.83 (Round to two decimal places as needed.) (ii) Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of 1600. (Round to two decimal places as needed.)
What critical value t∗t∗ from Table C would you use for a confidence interval for the mean of the population in each of the following situations? (a)96% confidence interval based on n = 25 observations.(b) A 95% confidence interval from an SRS of 17 observations.(c) A 90% confidence interval from a sample of size 13.
Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that ɛ P(X - ≤ μµ)≈ 0.95.
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(a) Find a sufficient statistic for 0. (b) Find the maximum likelihood estimator of 0. (c) Find a pivotal function of the maximum likelihood estimator found in (b). (d) Use the pivotal function obtained in (c) to construct a 100(1- a)% confidence interval for 0.